Monocular 3D detection's depth formula carries a systematic bias: MonoPCA corrects it in closed form and lifts KITTI moderate AP to 20.55

The geometric depth formula widely used in monocular 3D detection carries a systematic bias: it recovers the distance to an object's visible front surface, not to its center. Methods such as MonoFlex, MonoRCNN, GUP Net, MonoDETR, MonoDGP and MonoCoP all substitute the predicted 3D box height into the same projection relation, treating the formula as given and directing improvements to keypoint reasoning, geometric priors or uncertainty modeling around it. Even with ground-truth height, size and orientation as inputs, the formula leaves a depth error that grows monotonically with object size, indicating a structural rather than statistical origin; the bias is small for thin objects and severe for large vehicles.

PCDepth writes the discrepancy as the object's half-extent along the optical axis and derives a closed-form correction from orientation and size, recovering center depth from the measurable 2D box height. Regressing the center-aligned projected height directly is not viable because it is itself a function of the depth being sought, making the target circular and unstable; PCDepth instead retains the measurable 2D box height and closes the gap analytically. On the KITTI validation split at IoU 0.7 moderate difficulty, PCDepth reaches 26.22 AP, above direct regression at 23.82 and the original formula (GeoDepth) at 24.73; plugging PCDepth into MonoDETR, MonoDGP and MonoCoP pushes each above its published result.

Once depth is tied to predicted size and orientation, attribute perception becomes the new bottleneck, and GeoAlign distills geometric representations from a vision foundation model into a lightweight student. The lightweight backbones typical of monocular detectors underfit size and orientation estimation, while simply scaling up the backbone raises inference cost; GeoAlign lets a teacher fuse a convolutional hierarchy with EVA-CLIP and discards it after training. On the KITTI validation split, PCDepth and GeoAlign alone improve the baseline by 1.09 and 0.75 respectively, and together by 2.24, exceeding the sum of the individual gains; the cosine-based HFA alignment loss reaches 26.22, above MAE at 25.53 and MSE at 25.69.

The demonstrated scope is monocular 3D detection on four outdoor driving benchmarks: KITTI, nuScenes, Waymo and Omni3D. The student uses a ResNet-50 backbone, while the teacher fuses ResNet-50 with EVA-CLIP and is discarded after training, so inference cost does not increase. The closed-form correction assumes pinhole projection and an upright box, and treats the 2D box height as the tight projection of the eight 3D corners.

Truncation, occlusion and annotation tightness can make the 2D box height deviate from the tight projection of the eight corners, and this residual accounts for the error PCDepth still shows under oracle inputs. Depth now depends on predicted size and orientation, so attribute errors on heavily occluded or distant objects still propagate into depth; behavior under substantially different camera setups has not been studied.